Manuals/calci/HADAMARDPRODUCT

HADAMARDPRODUCT (a,b)

• $a$ and $b$ are any two matrices.

Description

• This function shows the value of the Hadamard product.
• In $HADAMARDPRODUCT(a,b)$,$a$ and $b$ are two matrices.
• Hadamard product is also called Schur product or entrywise product.
• The Hadamard product is associative,commutative and distributive.
• This product is the multiplied value of the each corresponding entries with the given two same dimension matrices.
• Hadamard product is defined by,For two matrices, A and B of the same dimension mxn, the Hadamard product $A\circ B$, is a matrix, of the same dimension as the operands, with elements given by:

$(A\circ B)_{i,j}=(A)_{i,j}(B)_{i,j}$

• Hadamard Product of order 2 is calculated by:

${\begin{pmatrix}a_{11}&a_{12}\\a_{21}&a_{22}\end{pmatrix}}$$\circ$ ${\begin{pmatrix}b_{11}&b_{12}\\b_{21}&b_{22}\end{pmatrix}}$ = ${\begin{pmatrix}a_{11}b_{11}&a_{12}b_{12}\\a_{21}b_{21}&a_{22}b_{22}\end{pmatrix}}$

Examples

1. HADAMARDPRODUCT([[2,3],[10,14]],[[6,4],[8,3]])

12	12
80	42

2. HADAMARDPRODUCT([[6,3,10],[5,-7,12],[4,2,6]],[[4,5,6],[9,2,-5],[12,13,7]])

24	15	60
45	-14	-60
48	26	42

See Also

• HADAMARD
• hadamard
• HANKEL

References

• Hadamard matrix

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